As a matter of fact, Zimbra Desktop does start, but the back-end fails (hence the UI does not display any screen as it cannot connect to the back-end).

I had it fixed by applying the following changes in "~/Library/Zimbra Desktop/bin/zdesktop":

line 480 : remove "-d32" from the options such that the 64-bits JVM will be executed;

before line 220, define JAVA_HOME (by adding a line "JAVA_HOME=/System/Library/Frameworks/JavaVM.framework/Home/").
Without this modification, the JVM was unable to load the NativeDB extension for SQLLite, failing to load existing data.